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研究生:周建國
研究生(外文):Chien-kuo Chou
論文名稱:限制下之雙變量零膨脹卜瓦松分布之研究
論文名稱(外文):The study of constrained bivariate zero-inflated Poisson distribution
指導教授:嵇允嬋嵇允嬋引用關係
指導教授(外文):Yun-Chan Chi
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:96
語文別:中文
論文頁數:45
中文關鍵詞:雙變量零膨脹卜瓦松分布截斷變數變換
外文關鍵詞:truncatedchange of variablesbivariate zero-inflated Poission distribution
相關次數:
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  • 下載下載:48
  • 收藏至我的研究室書目清單書目收藏:1
在應用雙變量機率分布時,通常會因為資料具有某些特殊限制,使得現有的雙變量機率分布的值域與資料不符合,因而造成機率分布無法合理地解釋資料。例如,一份探討四週內幼童因生病而未上學的天數與因病而在床上休息的天數之調查中,大多數幼童幾乎未生病或生病仍上學,故上述兩個天數大多為零,即所謂的零膨脹(zero-inflated)。此外,因生病而未上學的天數一定會大於或等於在床上休息的天數,此即資料所具有的特殊限制,所以Cheung 和 Lam (2006)將雙變量卜瓦松-卜瓦松分布(bivariate Poisson -Poisson distribution),以變數變換(change of variables)的方式推廣出在此限制下的機率分布。然而以此機率分布配適這組資料不如預期的好,所以本論文使用截斷(truncated)機率和變數變換的想法來推廣雙變量卜瓦松-卜瓦松分布和雙變量零膨脹卜瓦松分布(bivariate zero-inflated Poission distribution),使這些機率分布的值域具有跟資料相同的特殊限制。最後,以對數概似值(log-likelihood value)及卡方配適度檢定(goodness of fit test)來比較這些機率分布配適資料的結果。
Due to the constraints of the data, the range of the present bivariate probability distribution don’t correspond to the data when applying the bivariate probability distribution, and thus the probability distribution can not adequately explain the data. For example, a survey exploring the number of days that children couldn’t go to school because of illness and the number of days that children stayed in bed because of illness found that most children still went to school regardless of illness or no illness in the four weeks. Based on the above results, the number of days that children couldn’t go to school and the number of days that children stayed in bed were both zero mostly, which can be seen as zero-inflated. Besides, the number of days that children couldn’t go to school was absolutely greater or equal to that children stayed in bed, which is the constraint of the data. Therefore, Cheung and Lam (2006) developed a probability distribution within the constraints of the data by the change of variables from the bivariate Poisson-Poisson distribution, which didn’t result in the data allocating as well as expected, so finally the bivariate Poisson-Poisson distribution and the bivariate zero-inflated Poisson distribution were developed using truncated probability and the change of variables in this research in order to make the range of the probability distribution match the constraints of the data .Finally, this research adopted log-likelihood values and goodness of fit tests to compare the results of the data allocation of the probability distributions.
目錄 I
表目錄 III
圖目錄 IV
第一章 緒論 1
第二章 文獻探討 4
第一節 雙變量卜瓦松-卜瓦松分布 4
第二節 雙變量卜瓦松分布 5
第三節 雙變量零膨脹卜瓦松分布 6
第四節 限制下之BPP分布 8
第五節 機率分布評比之檢定 9
第三章 BP與BPP分布之推廣 12
第一節 截斷機率分布 12
第二節 BPP分布之推廣一 14
第三節 BPP分布之推廣二 15
第四節 BZIP分布之推廣一:變數變換 16
第五節 BZIP分布之推廣二:截斷 18
第六節 參數估計 21
第四章 資料分析 22
第一節 應用BPP和BPP-CL分布於幼童資料 22
第二節 應用推廣之機率分布配適幼童資料 24
第三節 配適平交道資料 26
第五章 結論與建議 28
參考文獻 29
附錄一 30
附錄二 41
Cheng, Y.B. and Lam, K.F. (2006), “Bivariate Poisson-Poisson model of zero-inflated absenteeism data,” STATISTICA IN MEDICINE, Vol. 35, pp. 525-529.
Kui, W., Andy, H.L., Kelvin, K.W. and Philip, J.W. (2003), “A bivariate Zero-inflated Poisson Regression Model to analysis occupational injuries,” ACCIDENT ANALYSIS & PREVENTION, Vol. 35, pp. 625-629.
Li, C.S., Lu, J.C., Park, J., Kim, K., Boinkley, P.A. and John, P. (1999), “Multivariate Zero-Inflated Poisson Models and Their Applications,” Technometrics, Vol. 41, pp.29-38.
Loukas, S. and Kemp, C.D. (1986), “On the Chi-Square Goodness of Fit statistic for Bivariate Discrete Distributions,” The Statistician, Vol. 35, pp. 525-529.
Steven, Y., David, E.M. and Smith, J.E. (1991), “Analysis of Multinomial Misture Distributions: New Tests for Stochastic Models of Cognition and Action,” Psychoiogical Bulletin, Vol. 110, pp. 250-274.
Vuong, Q.H. (1989), “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses,” Econometrica, Vol. 57, pp. 307-333.
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